{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "c38b58ad",
   "metadata": {},
   "source": [
    "<a href=\"https://sm.ms/image/lPoAzTFncsHMIKy\" target=\"_blank\"><img src=\"https://s2.loli.net/2022/06/24/lPoAzTFncsHMIKy.jpg\" ></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "3b451a89",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "d9c3ad6b",
   "metadata": {},
   "outputs": [],
   "source": [
    "#赋初值\n",
    "D = 1\n",
    "miu = 40 * D\n",
    "E = 10\n",
    "tuo = 0.01\n",
    "dx = 0.01\n",
    "dt = 0.00001\n",
    "\n",
    "n = 4000\n",
    "m = 2000 * dx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "fec4ebc8",
   "metadata": {},
   "outputs": [],
   "source": [
    "#定义e指数函数\n",
    "def uBegin(x):\n",
    "    return 1/np.sqrt(2*np.pi)/200/dx*np.exp(-x**2/2/(200*dx)**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "fa07d0ef",
   "metadata": {},
   "outputs": [],
   "source": [
    "sigma = D * dt / (dx ** 2)\n",
    "gama = miu * E * dt / dx\n",
    "beita = dt / tuo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "fdc772d7",
   "metadata": {},
   "outputs": [],
   "source": [
    "xArr = np.arange(-m,m + dx,dx)\n",
    "tArr = np.arange(0,n * dt,dt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "8e0c24ff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4002, 4000)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xArr.size,tArr.size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "1b700ac9",
   "metadata": {},
   "outputs": [],
   "source": [
    "A = np.identity(xArr.size - 2)\n",
    "\n",
    "B = np.roll(A,1)\n",
    "B[0,0] = 0\n",
    "\n",
    "C = np.roll(A,-1)\n",
    "C[-1,-1] = 0\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "422f3657",
   "metadata": {},
   "outputs": [],
   "source": [
    "A1 = (1-2*sigma-gama-beita)*A + (sigma + gama) * B + sigma * C"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "b6f6cd99",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4000, 4000)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A1.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "c63b7efc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "bVector = np.zeros(xArr.size - 2)\n",
    "uCurrent = uBegin(xArr[1:-1])\n",
    "plt.plot(xArr[1:-1],uCurrent)\n",
    "uArr = np.zeros((xArr.size - 2,tArr.size))\n",
    "uArr[:,0] = uCurrent\n",
    "for i in range(4000):\n",
    "    uNext = A1 @ uCurrent + bVector\n",
    "    uArr[:,1] = uNext\n",
    "    plt.plot(xArr[1:-1],uNext)\n",
    "    uCurrent = uNext"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "b83854f0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x26dc40206d0>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(uArr)\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "9151b7e4",
   "metadata": {},
   "outputs": [],
   "source": [
    "A2 = (1+2*sigma+gama+beita)*A - (sigma+gama)*B - sigma*C"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "f63347dd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4000, 4000)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A2.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "c07d46f5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "AInv = np.linalg.inv(A2)\n",
    "bVector = np.zeros(xArr.size - 2)\n",
    "uCurrent = uBegin(xArr[1:-1])\n",
    "plt.plot(xArr[1:-1],uCurrent)\n",
    "uArr = np.zeros((xArr.size - 2,tArr.size))\n",
    "uArr[:,0] = uCurrent\n",
    "for i in range(4000):\n",
    "    uNext = AInv @ uCurrent + AInv @ bVector\n",
    "    uArr[:,1] = uNext\n",
    "    plt.plot(xArr[1:-1],uNext)\n",
    "    uCurrent = uNext"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "5158995a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x26dcebf74f0>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(uArr)\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "1a7fad96",
   "metadata": {},
   "outputs": [],
   "source": [
    "A3 = (1+D*dt/dx**2+dt*miu*E/dx)*A -(dt*miu*E/dx+D*dt/2/dx**2)*B - (dt*D/2/dx**2)*C\n",
    "A4 = (1-D*dt/dx**2)*A + (D*dt/2/dx**2)*B + (D*dt/2/dx**2)*C\n",
    "AF = A3 @ A4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "801faf54",
   "metadata": {},
   "outputs": [
    {
     "ename": "IndexError",
     "evalue": "invalid index to scalar variable.",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mIndexError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[1;32m~\\AppData\\Local\\Temp/ipykernel_17052/2127035948.py\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      8\u001b[0m \u001b[0mA3\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mlinalg\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0minv\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mA1\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m@\u001b[0m \u001b[0mA2\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      9\u001b[0m \u001b[0muArr\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mzeros\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mxArr\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msize\u001b[0m \u001b[1;33m-\u001b[0m \u001b[1;36m2\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtArr\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msize\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 10\u001b[1;33m \u001b[0muArr\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0muBegi\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     11\u001b[0m \u001b[0muCurrent\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0muArr\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     12\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mIndexError\u001b[0m: invalid index to scalar variable."
     ]
    }
   ],
   "source": [
    "bVector = np.zeros(xArr.size - 2)\n",
    "uCurrent = uBegin(xArr[1:-1])\n",
    "plt.plot(xArr[1:-1],uCurrent)\n",
    "uArr = np.zeros((xArr.size - 2,tArr.size))\n",
    "uArr[:,0] = uCurrent\n",
    "for i in range(4000):\n",
    "    uNext =AF@(uCurrent+bVector)\n",
    "    uArr[:,1] = uNext\n",
    "    plt.plot(xArr[1:-1],uNext)\n",
    "    uCurrent = uNext"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1c9afa65",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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